Optical and resonant X-ray diffraction studies confirm a SmC*FI2-SmC* liquid crystal phase sequence reversal

Employing both null transmission ellipsometry and resonant x-ray diffraction, we confirmed the SmC*FI2-SmC* phase sequence reversal in one liquid crystal compound and specially prepared binary mixtures. This phase sequence reversal was predicted by two recent theoretical advances. Moreover, the temperature range for the SmC*FI2 phase increases significantly in the mixture suggesting that such a phase sequence may exist in other compounds.     

Spaces of lower semicontinuous set-valued maps I

We introduce a lower semicontinuous analog, L ^?(X), of the well-studied space of upper semicontinuous set-valued maps with nonempty compact interval images. Because the elements of L ^?(X) contain continuous selections, the space C(X) of real-valued continuous functions on X can be used to establish properties of L ^?(X), such as the two interrelated main theorems. The first of these theorems, the Extension Theorem, is proved in this Part I. The Extension Theorem says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L ^?(X) and L ^?(Y). The second main theorem, the Factorization Theorem, is proved in Part II. The Factorization Theorem says that for binormal spaces X and Y, every ordered homeomorphism between L ^?(X) and L ^?(Y) can be characterized by a unique factorization.     

Function spaces and product topologies on powers of spaces

A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces.     

A theoretical and computational study of the anion, neutral, and cation Cu(H(2)O) complexes

An ab initio investigation of the potential energy surfaces and vibrational energies and wave functions of the anion, neutral, and cation Cu(H(2)O) complexes is presented. The equilibrium geometries and harmonic frequencies of the three charge states of Cu(H(2)O) are calculated at the MP2 level of theory. CCSD(T) calculations predict a vertical electron detachment energy for the anion complex of 1.65 eV and a vertical ionization potential for the neutral complex of 6.27 eV. Potential energy surfaces are calculated for the three charge states of the copper-water complexes. These potential energy surfaces are used in variational calculations of the vibrational wave functions and energies and from these, the dissociation energies D(0) of the anion, neutral, and cation charge states of Cu(H(2)O) are predicted to be 0.39, 0.16, and 1.74 eV, respectively. In addition, the vertical excitation energies, that correspond to the 4 (2)P<--4 (2)S transition of the copper atom, and ionization potentials of the neutral Cu(H(2)O) are calculated over a range of Cu(H(2)O) configurations. In hydrogen-bonded, Cu-HOH configurations, the vertical excitation and ionization energies are blueshifted with respect to the corresponding values for atomic copper, and in Cu-OH(2) configurations where the copper atom is located near the oxygen end of water, both quantities are redshifted.     

Reactive scattering dynamics in atom+polyatomic systems: F+C2H6-->HF(v,J)+C2H5

State-to-state scattering dynamics of F+C2H6-->HF(v,J)+C2H5 have been investigated at Ecom=3.2(6) kcalmol under single-collision conditions, via detection of nascent rovibrationally resolved HF(v,J) product states with high-resolution infrared laser absorption methods. State-resolved Doppler absorption profiles are recorded for multiple HF(v,J) transitions originating in the v=0,1,2,3 manifold, analyzed to yield absolute column-integrated densities via known HF transition moments, and converted into nascent probabilities via density-to-flux analysis. The spectral resolution of the probe laser also permits Doppler study of translational energy release into quantum-state-resolved HF fragments, which reveals a remarkable linear correlation between (i) HF(v,J) translational recoil and (ii) the remaining energy available, Eavail=Etot-E(HF(v,J)). The dynamics are interpreted in the context of a simple impulsive model based on conservation of linearangular momentum that yields predictions in good agreement with experiment. Deviations from the model indicate only minor excitation of ethyl vibrations, in contrast with a picture of extensive intramolecular vibrational energy flow but consistent with Franck-Condon excitation of the methylene CH2 bending mode. The results suggest a relatively simple dynamical picture for exothermic atom+polyatomic scattering, i.e., that of early barrier dynamics in atom+diatom systems but modified by impulsive recoil coupling at the transition state between translationalrotational degrees of freedom.     

Connection formulae for Painlevé V functions : II. The δ function Bose gas problem

We continue our study of those Painlevé V equations which admit a one-parameter family of solutions analytic at the origin and solve the global problem of connecting the 2-parameter expansion about t = 0 with the 2-parameter expansion valid for t → ± i∞. A special case of our results is applied to the study of the one-particle reduced density matrix of the one-dimensional gas of impenetrable bosons. We also use our results to obtain a 2-parameter connection formula for a class of Painlevé III functions.     

Improved Resolution from Double Constant-Time Evolution of 3D and 4D Triple-Resonance Experiments

Triple-resonance NMR experiments are nearly essential for performing backbone assignments of proteins larger than 15 kDa. Our work extends the double constant-time (2CT) evolution scheme to triple-resonance 3D and 4D experiments. The modifications needed to accomplish 2CT evolution in triple resonance experiments are straight forward, are completely general, and consequently, will yield increased resolution for all out-and-back experiments. We expect that the increased resolution of experiments presented here will be useful in the study of larger proteins (>30 kDa) and in the study of highly helical proteins where¹HN,¹⁵N, and¹³C dimensions are poorly dispersed.     

Accelerating networks: Effects of preferential connections

Networks are commonly observed structures in complex systems with interacting and interdependent parts that self-organize. For nonlinearly growing networks, when the total number of connections increases faster than the total number of nodes, the network is said to accelerate. We propose a systematic model for the dynamics of growing networks represented by distribution kinetics equations. We define the nodal-linkage distribution, construct a population dynamics equation based on the association-dissociation process, and perform the moment calculations to describe the dynamics of such networks. For nondirectional networks with finite numbers of nodes and connections, the moments are the total number of nodes, the total number of connections, and the degree (the average number of connections per node), represented by the average moment. Size independent rate coefficients yield an exponential network describing the network without preferential attachment, and size dependent rate coefficients produce a power law network with preferential attachment. The model quantitatively describes accelerating network growth data for a supercomputer (Earth Simulator), for regulatory gene networks, and for the Internet.